A109622 Number of different isotemporal classes of diasters with n peripheral edges.

1, 1, 4, 7, 15, 23, 38, 53, 77, 101, 136, 171, 219, 267, 330, 393, 473, 553, 652, 751, 871, 991, 1134, 1277, 1445, 1613, 1808, 2003, 2227, 2451, 2706, 2961, 3249, 3537, 3860, 4183, 4543, 4903, 5302, 5701, 6141, 6581, 7064, 7547, 8075, 8603

Offset

0,3

Comments

See A092481 for the definition of isotemporal classes.

References

Benjamin de Bivort, Isotemporal classes of diasters, beachballs and daisies, preprint, 2005.

Links

Table of n, a(n) for n=0..45.

Formula

a(n=2k) = 1 + sum_{i=1}^{(n/2)-1} (n*i-i^2+n+1) + (1/2)((n/2)^2+3(n/2)+2) a(n=2k+1)= 1 + sum_{i=1}^{(n-1)/2} ((n*i-i^2+n+1). [Corrected by Sean A. Irvine after private communication with Benjamin de Bivort, Feb 13 2012]

a(n) = A005993(n) - n. - Enrique Pérez Herrero, Apr 22 2012

Example

A diaster is defined to be any graph with a central edge with vertices of degree j and k and j+k peripheral edges connected to the central edge each terminating in a vertex of degree 1. a(5)=23 refers to diasters with 5 peripheral edges. These can be uniquely arranged with 0, 1 or 2 peripheral edges on a particular side, yielding 1, 10 and 12 isotemporal classes respectively each.

Crossrefs

Cf. A092481, A005993.

Sequence in context: A271675 A356714 A039669 * A269967 A124286 A235603

Adjacent sequences: A109619 A109620 A109621 * A109623 A109624 A109625

Keyword

nonn,easy

Author

Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 02 2005

Extensions

More terms from Sean A. Irvine, Feb 12 2012

Status

approved